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Canonical Quantization of QFT
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Module 3
Fermionic Fields and Quantum Electrodynamics (QED)
1
Dirac Equation and Plane-Wave Solutions
Derive the Dirac equation and construct its plane-wave spinor solutions for particles and antiparticles.
2
Quantizing the Free Dirac Field
Formulate the Lagrangian for the free Dirac field and quantize it by imposing equal-time anti-commutation relations.
3
Fermionic Fock Space and Pauli Exclusion
Construct the Fock space for fermions, demonstrating the Pauli exclusion principle.
4
Feynman Propagator for the Dirac Field
Derive the Feynman propagator for the Dirac field.
5
Deriving the QED Interaction from U(1) Gauge Invariance
Introduce the principle of local U(1) gauge invariance for the Dirac Lagrangian to derive the QED interaction term.
6
Covariant Quantization of the Electromagnetic Field
Quantize the electromagnetic field in a covariant gauge (e.g., Lorenz gauge) and derive the photon propagator.
7
Building the QED Lagrangian
Construct the complete QED Lagrangian, identifying the interaction vertex.
8
Feynman Rules for Tree-Level QED
State the complete set of Feynman rules for tree-level QED in momentum space.
Previous module
Interacting Fields and Perturbative Scattering
Next module
Tree-Level Processes in QED